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Prove that cos55^0+cos65^0+cos175^0=0...

Prove that `cos55^0+cos65^0+cos175^0=0`

Text Solution

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LHS`=cos55^(@)+cos 65^(@)+cos175^(@)`
`=2cos(55^(@)+65^(@))/(2)cos(55^(@)-65^(@))/(2)+cos175^(@)`
`=2cos 60^(@)cos(-5^(@))+cos175^(@)`
`=2xx(1)/(2)cos5^(@)+cos(180^(@)-5^(@))`
`=cos5^(@)-cos5^(@)=0`
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